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I don't have a favorite civ...

In civ V, I have 3. I like a civ that either A) Has such a strong early game it helps me get through and maybe do stuff I otherwise couldn't (Babylon), B) allows me to play differently in a unique and fun way (civ V's Mongols) or C) has just such strong bonuses that it can carry me (civ V's England, believe it or not, my first diety win).

But I don't feel any civs are like that in VI. And though I love the game, I still haven't found a civ I like yet.

If you want just generally strong bonuses and powerful early games, you can't go wrong with Nubia or Greece imo. Greece has an amazing start bias (hills), and Nubia has a unique archer which is amazing for early wars. They can set themselves up for any victory type pretty easily, and both have bonuses that are useful throughout the game.

America is very overlooked, but that home continent bonus is excellent in the early game and film studios/national parks are nice for a final culture run. Founding Fathers sucked in base but is a lot better now.

I'm absolutely loving Eleanor right now. I'm annexing whole continents, I just do love how this works. I'm also really enjoying her rose color (one of my requirements is the civ has ti be aesthetically pleasing lol)

I don't either, and that's not a bad thing. Though it could be if you see the game as less challenging than Civ 5 (and it is very much less challenging). Nearly all of them I enjoy except Nubia and Scythia.

"Human behavior is economic behavior. The particulars may vary, but competition for limited resources remains a constant. Need as well as greed have followed us to the stars, and the rewards of wealth still await those wise enough to recognize this deep thrumming of our common pulse."

Don't think it's a bad thing not to have a favourite civ - possibly too easy to choose them by default for every game, or go the opposite approach and just select the easiest 'obvious' civ for each VC, e.g. Korea science.
Personally I do have a fave civ but I tend to play them in silly ways when I can't be arsed to play properly.
There's a lot to be said for random civs/maps, it makes you think and adapt.

Here are some civs that have bonuses similar to the civs you favored in Civ 5.

Babylon
Free Early Great Scientist: Check out Korea. They have a unique science district that costs only half the normal production to make and always has max adjacency bonuses. They also have a way to generate science from mines.Faster Great Scientists: Maybe try Brazil. They generate all great people faster than anyone else, after the first one. Sweden also gets a small bonus to earning great scientists once they start building universities.Stronger Archer: Nubia has a unique archer.Stronger Ancient Walls: There is currently no civ that has unique ancient walls, but Georgia has unique renaissance walls.

Mongolia
Extra Combat Strength Against City-States: Germany has this exact same ability.Cavalry Have Extra Movement: The Civ 6 version of Mongolia has a unique stable that grants this same ability.Unit That Grants Great General Points From Kills: Macedon has a unique unit that does this, although it comes an era earlier.Great Generals Increase Combat Strength More: The same Macedonian unit I mentioned above also gets more combat strength from Great Generals than normal.

England
Boats Have Extra Movement: The Civ 6 version of England has a unique harbor that grants this same ability. Indonesia has a unique renaissance era ship with extra movement.Extra And Earlier Spy: France has this ability, but only when Catherine de Medici is leading.Longer Range Crossbowman: I cannot think of any civilizations that have an ability or unique unit similar to this.Stronger Frigate: Both the Netherlands and Indonesia have unique frigates.

I'm absolutely loving Eleanor right now. I'm annexing whole continents, I just do love how this works. I'm also really enjoying her rose color (one of my requirements is the civ has ti be aesthetically pleasing lol)

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I didn't really find her ability that overpowering. Cities started dropping once I captured the big cities, say their capital, but I was expecting cities to just be falling like crazy based on people here and I just didn't see it happening. Maybe I just wasn't crowding them out enough.

I keep moving my Great Works to my frontier cities, and I do have a couple surrounding my targets. And I'm also using Amani for some extra pressure, and Bread & Circuses. But it's like once cities start flipping, you just start rolling ... and when you skip that Free City stage, that's a huge bonus! I've just about wiped out Nubia, and I've taken over half of the Zulus without even having to attack one city

I keep moving my Great Works to my frontier cities, and I do have a couple surrounding my targets. And I'm also using Amani for some extra pressure, and Bread & Circuses. But it's like once cities start flipping, you just start rolling ... and when you skip that Free City stage, that's a huge bonus! I've just about wiped out Nubia, and I've taken over half of the Zulus without even having to attack one city

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I didn't try using bread and circuses but did everything else. Maybe that is what I was missing.

Aztecs are my fave. Be an early aggressor and get some free workers. Just build two more eagle warriors, a slinger for the eureka, two more eagles and two more slingers. Then just eat you neighbors like Audrey II (yeah I'm old enough for a Little Shop reference, "Feed me Seymour!"). Research archery once you get that third slinger. Archers are great for whittling units down for your Eagles to get the kill. Once the medieval kicks in you can either continue munching on competitors or pick a VC to coast to. Lots of fun.

Currently trying out the new civs one by one but after I get a win with each I'll probably head back to random. Don't really feel like going down the list to fill the HoF asap.

Early man walked away as modern man took control.
Their minds weren't all the same, to conquer was his goal,
So he built his great empire and slaughtered his own kind,
Then he died a confused man, killed himself with his own mind​

I pretty much only go for passive victory types (i.e. I don't want to move a ton of units all the time), so science, culture, or diplomacy civs. I also love building + infrastructure. So my favorite civs end up being things like the Dutch, Inca, Australia, France, etc.

I definitely have favorite civs in Civ6 (Georgia, Norway, Spain), but because of other criteria.
I feel like too many civs fulfill your requirements. I don't know the Civ5 gameplay, but:
A) Aztec - extra strength early and possible free builders you can use for districts.
B) Kongo. There are too few really generic civs, so this was hard to choose. I discovered each civ gives a unique experience (some like Germany I simply cannot play due to this).
C) America, maybe?